Let's suppose that we are interested in the random variable T = mile time of a randomly selected person. In this case, the expected value u = E[T] is not well defined since some people cannot complete a mile. So, we can instead let T = mile time of a randomly selected person given that the selected person completes the mile (a conditional random variable).

What can we say about the distribution of T? For one, it almost assuredly is not symmetric around the mean u = E[T]. In fact, it is heavy-tailed and 'more' of the distribution is to the right of the mean u.

What else? Well, it is multimodal, meaning the density of T will have multiple peaks, since different sub-populations will have their own unique, non-overlapping characteristics. I expect there to be modes at around 4:02 (for pro milers), 4:30 (for college milers), 8:00 (for hobby joggers), and 12 (for non-runners).